I checked 3 different Siddurim for instructions regarding how to respond to parts of the Kedusha. All are Nusach Ashkenaz
Art Scroll has inconsistent rules:
Weekday Kedusha Shacharit & Mincha
Cong. then chazzan say נקדש
Cong. and chazzan say קדוש together ; Chazzan only לעומתם
Cong. and chazzan say ברוך together ; Chazzan only ובדברי
Cong. and chazzan say ימלוך together
Shabbat Shacharit and Musaph Kedusha
Cong. then chazzan say נקדש
All other paragraphs are said by cong. followed by Chazzan
I don't know why Art Scroll has different rules for weekday and Shabbat. Is this an error?
Birnbaum
All paragraphs are cong. followed by the chazzan
Chayim Shlomo
For the weekday Kedusha (I haven't checked what he does for Shabbat, and, B"N, I'll edit it in later):
Cong. then chazzan say נקדש
Cong. then chazzan say קדוש ; Chazzan only לעומתם
Cong. then chazzan say ברוך ; Chazzan only ובדברי
Cong. then chazzan say ימלוך
In summary, there seem to be 3 versions of what to do after the 1st paragraph. (All agree that the Cong. starts the Kedushah)
Version 1 - Alternate starting with the 2nd paragraph with 2nd said by Cong. then Chazan, 3rd only Chazzan, 4th Cong. then Chazzan, etc.
Version 2 - Same as version 1, except that 2nd, 4th, 6th, etc. are said by Chazzan & Cong. together
Version 3 - All paragraphs are done by Cong. then by chazzan
So, which version is correct, or are all acceptable?